Circular Motion Test. 1

Moment of inertia (I) measures an object's resistance to changes in its rotational motion, just as mass measures resistance to changes in linear motion.

A full circle is 2π radians (360°), so half a circle (180°) is π radians.

Specifically, τ = r × F. The order is important in a cross product.

Acceleration is the rate of change of velocity. If angular velocity is constant, its rate of change is zero.

This is the critical velocity needed to maintain a low Earth orbit, balancing gravity's pull.

This is the time it takes for the Earth to complete one rotation on its axis, so the satellite's period must match.

Curl the fingers of your right hand in the direction of rotation; your thumb points in the direction of the angular velocity vector.

This is the rotational analogue of the linear kinetic energy formula, with mass replaced by moment of inertia (I) and velocity by angular velocity (ω).

Radian is the standard international (SI) unit for measuring angles in physics.

Angular momentum (L = r × p) has dimensions of radius [L] times linear momentum [MLT⁻¹], resulting in [ML²T⁻¹].

This is the law of conservation of angular momentum, the rotational analogue to the conservation of linear momentum.

Both the astronaut and the station are continuously falling towards Earth but have enough tangential velocity to miss it, creating the sensation of weightlessness.

This shows that for a given angular velocity, the linear (tangential) velocity is greater at a larger radius.

This acceleration is responsible for continuously changing the direction of the velocity vector to keep the object on a circular path.

When the road is banked, the normal force has a horizontal component pointing towards the center of the curve, providing the centripetal force.

Rotation creates a centripetal force on occupants, which they perceive as a 'gravity-like' force pushing them towards the outer wall.

To appear stationary from the ground, it must complete one orbit in the same time the Earth completes one rotation.

Since all the mass of the hollow sphere is at the maximum radius, its moment of inertia (I = 2/3 MR²) is greater than the solid sphere's (I = 2/5 MR²).

The farther the mass is from the axis of rotation, the greater the moment of inertia (I = Σmᵢrᵢ²).

This is the net force, directed towards the center, that is required to cause circular motion.